Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres

A Bell experiment that is ‘loophole’ free—leaving no room for explanations based on experimental imperfections—reveals a statistically significant conflict with local realism A new test of the Bell inequality The celebrated Bell inequality, a theorem published by John Bell in 1964, has long served as a basis for experimentally testing whether nature satisfies local realism. All experiments conducted to date have implied rejection of local-realist hypotheses. But because of experimental limitations all those tests suffered from loopholes — either the locality or the detection loophole. Here, Ronald Hanson and colleagues perform a Bell test that closes these loopholes. Their results are consistent with a violation of the inequality, although the authors reject local-realist hypotheses by two standard deviations only. The experimental setup allows for improvements in the statistics that may consolidate the result. In addition to its fundamental importance, a loophole-free Bell test is an important building block in quantum information processing. More than 50 years ago 1 , John Bell proved that no theory of nature that obeys locality and realism 2 can reproduce all the predictions of quantum theory: in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled. Numerous Bell inequality tests have been reported 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in ‘loopholes’ 13 , 14 , 15 , 16 . Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell’s inequality. We use an event-ready scheme 17 , 18 , 19 that enables the generation of robust entanglement between distant electron spins (estimated state fidelity of 0.92 ± 0.03). Efficient spin read-out avoids the fair-sampling assumption (detection loophole 14 , 15 ), while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 kilometres ensure the required locality conditions 13 . We performed 245 trials that tested the CHSH–Bell inequality 20 S ≤ 2 and found S = 2.42 ± 0.20 (where S quantifies the correlation between measurement outcomes). A null-hypothesis test yields a probability of at most P = 0.039 that a local-realist model for space-like separated